With the emergence of applications based on short-wavelength infrared light, indium arsenide quantum dots are promising candidates to address existing shortcomings of other infrared-emissive nanomaterials. However, III-V quantum dots have historically struggled to match the high-quality optical properties of II-VI quantum dots. Here we present an extensive investigation of the kinetics that govern indium arsenide nanocrystal growth. Based on these insights, we design a synthesis of large indium arsenide quantum dots with narrow emission linewidths. We further synthesize indium arsenide-based core-shell-shell nanocrystals with quantum yields up to 82% and improved photo- and long-term storage stability. We then demonstrate non-invasive through-skull fluorescence imaging of the brain vasculature of murine models, and show that our probes exhibit 2-3 orders of magnitude higher quantum yields than commonly employed infrared emitters across the entire infrared camera sensitivity range. We anticipate that these probes will not only enable new biomedical imaging applications, but also improved infrared nanocrystal-LEDs and photon-upconversion technology.